Question

Find the square root of the below number using the prime factorization method.
3136

Answer 1

Hint: In this question, we go step by step-
First, we divide the 3136 into its prime factor.
Make the pair of similar factors such that the both factors in each pair are equal.
Pick out one factor from each pair.
We will find the product of factors obtained by taking one factor from each pair.
That product is equal to the square root of the given number.

Complete step-by-step answer:
Let’s divide 3136 into prime factors.
$3136 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7$
Now, we make pairs;
$ \Rightarrow \left( {2 \times 2} \right) \times \left( {2 \times 2} \right) \times \left( {2 \times 2} \right) \times \left( {7 \times 7} \right)$
Taking one factor from each pair:
$ \Rightarrow $$2 \times 2 \times 2 \times 7$
Product of factors = 56
Thus, $\sqrt {3136} = 56$.

Note: Prime factorization is a method of factoring a number in terms of prime numbers that is the factors will be prime numbers. Prime factorization is a way of finding the prime factors of a number that is prime numbers which can be multiplied together to get the original number. Prime factorization of 24 is $2 \times 2 \times 2 \times 3$. When prime numbers when multiplied by any natural numbers or whole numbers, gives composite numbers. Prime factors can divide the number completely. There are two types of prime factorization methods: 1) Division Method 2) Factor Tree method.
Division Method – In this method we will divide the given number by the smallest prime number. Again, we will divide the quotient by the smallest prime number. We will repeat the process until the quotient becomes 1. Finally, we will multiply all the prime factors.